Trajectory planning system for a vehicle and vehicle

A trajectory planning system for a vehicle comprising:

• a sensor system for measuring an actual curvature on a basis of a respective current actual yaw rate;
• a memory containing a target trajectory with target curvatures;
• a steering system with steering variables configured to be applied to an actual curvature to obtain the target curvatures using the steering variables;
• and
• at least one processing device configured to:
• determine target yaw rates from the target curvature in the target trajectory;
• determine a respective first actual derivative of the measured respective current actual yaw rate over time and a respective first target derivative of the respective current target yaw rate over time;
• determine a respective current delay on a basis of the respective first actual derivative and the respective first target derivative in a current yaw rate segment;
• recursively estimate an estimated delay between the target yaw rate and the actual yaw rate on a basis of respective current delay inputs;
• and
• determine a time period on a basis of at least the estimated delay in relation to the actual curvature, in order to compensate for a delay while obtaining the target curvature by applying the steering variables to the actual curvature.